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Hps2205:Quantitative Methods Question Paper
Hps2205:Quantitative Methods
Course:Bachelor Of Commerce
Institution: Meru University Of Science And Technology question papers
Exam Year:2013
QUESTION ONE (30 MARKS)
a) i) Define a set and give an illustration on the application of set theory in business and management. (4 Marks) ii) Given that = {1,2,3} = {2 3 4 5} = {5,7} = {:1 12, } Evaluate the following operations and then present them in a Venn diagram shading the wanted regions. i. ii. iii. ( ) (6 Marks) b) Solve for x given that i. 3 22 = 0 (3 Marks) ii. = log64 4 (1 Mark) iii. 2 + 7 1 2 15 = 0 (3 Marks) c) The sum of the first three terms of a sequence is 26. If the common ratio is 3, find the sum of the first 6 terms. (5 Marks)
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d) Distinguish between each of the following terms; i. Descriptive and inferential statistics ii. Primary and secondary data iii. Continuous and discrete variables iv. Population and sample. (8 Marks)
QUESTION TWO (20 MARKS)
a) The following data relates to the profit realized by 30 firms in thousands of shillings 28 35 61 29 36 48 57 67 69 50 48 40 47 42 41 37 51 62 63 33 31 32 35 40 38 37 60 51 54 56 i. Taking 25 – 29, 30 – 34 etc as class intervals, construct a frequency distribution table for the data. (4 Marks) ii. State the modal class. (1 Mark) iii. Calculate the mean and the standard deviation. (6 Marks) iv. Present the data using a Histogram and estimate the mode. (4 Marks) v. Comment on the distribution of the data using iv) above. (1 Mark)
b) Solve for x and y given 3 2 = 0 2 = 4 (4 Marks)
QUESTION THREE (20 MARKS)
a) A woman saves 20 dollars per month from age 22 to 65. If her savings earn interest at a rate of 6.6% p.a compounded monthly, how much does she has at retirement. (5 Marks) b) Population in a 3rd world country is growing continuously at a rate of 3%. If the population stands at 4.5million,what will it be in 15 years time? (5 Marks) c) Find the future value and the amount of interest earned by a deposit of 900 shillings for 8 years compounded semi annually. (5 Marks) d) Joan must pay a lumpsum of Ksh. 6000 in 8 years. What lumpsum deposited today at 4% compounded annually will amount to ksh. 6000 in 8 years. (5 Marks)
QUESTION FOUR (20 MARKS)
a) A group of 60 students at MUST were surveyed with the following results. 19 of the students read business week 18 read the Journal 50 read Forture 13 read Business week and the Journal 11 read the Journal and the Forture 13 read the Business week and Forture
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9 read all the three
Required:
i. Present the information on a Venn diagram. (3 Marks)
Using the Venn diagram;
Determine:
ii. The number of student who read none of the publication. (1 Mark) iii. The number of the students who read exactly one of the publications. (2 Marks) iv. The number of the student who read Business week or the Journal but not Forture. (2 Marks) b) A competitive market has the demand schedule P=610-3q and the supply schedule P=50+4q where P is the price in shillings and q is the quantity in units. Find the equilibrium values of p and q. (4 Marks) c) Discuss the four levels of measurements. (8 Marks)
QUESTION FIVE (20 MARKS)
a) Solve by elimination method; 2 + = 2 + 3 + 2 = 1 + + 2 = 2 b) A theatre charges ksh. 4 for the main floor seats and ksh.2.50 for balcony seats. If all the seats are sold the income is ksh. 2100. At one show, 25% of the main floor seats and 40% of the balcony seats were sold and the ticket income realized was ksh.600. How many seats on the main floor and balcony were sold? (4 Marks) c) i) List three properties of a good average. (3 Marks) ii) List two properties of a normally distributed data. (2 Marks) d) The data below shows the distribution of weight of female and male workers in a firm. Female Male Number 50 100 Average weight 65kg 60kg Standard deviation 35kg 3kg i. Determine the coefficient of variation for both male and male workers. (4 Marks) ii. Which of the sex shows a greater variability in weight? (1 Mark)
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